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Unformatted text preview: what happens when the minimum input constraint binds: Iso-cost line
when minimum
input constraint
binds Iso-cost line
when minimum
input constraint
did not bind Target
Output 0 28
ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The cost of production with a binding minimum input 1 constraint is higher than the cost with a non-binding minimum
input 1 constraint. This is intuitive because for whatever reason the firm has to use a minimum amount of input 1 which
here happens to be greater than the unconstrained amount of input 1 and the firm must bear the cost of using “excess
amount” of input 1 and so (how do you know that ?): ⏟ At the optimum, the price of input 1 must be the sum of marginal cost of using it for production plus the marginal cost
due to “excessive usage”.
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Having established some general results by using the envelope theorem we now discuss ways to simplify the long run
CMP (ways to cut down the number of KT cases one has to check):
(
⏟ ∑( ) )( [ ) ⏟ ( ) ∑ As in consumer theory UMP, we look for ways to “drop” one, some, or hopefully all the “non-negativity” constrain...
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